Madhukesh J K

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These are questions asked by Madhukesh J K

Hi

I got the error like this unable to convert to an explicit first-order system

please anyone can help me to solve this

I am attaching the worksheet

with(plots); restart

eq1 := (2*eta*gamma+1)*(diff(f(eta), `$`(eta, 3)))+2*gamma*(diff(f(eta), `$`(eta, 2)))+f(eta)*(diff(f(eta), `$`(eta, 2)))-(diff(f(eta), eta))^2-(Q+S)*(diff(f(eta), eta))+beta*(diff(F(eta), eta)-(diff(f(eta), eta))) = 0;

(2*eta*gamma+1)*(diff(diff(diff(f(eta), eta), eta), eta))+2*gamma*(diff(diff(f(eta), eta), eta))+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-(Q+S)*(diff(f(eta), eta))+beta*(diff(F(eta), eta)-(diff(f(eta), eta))) = 0

(1)

eq2 := (diff(F(eta), `$`(eta, 2)))*F(eta)-(diff(F(eta), eta))^2+beta*(diff(f(eta), eta)-(diff(F(eta), eta))) = 0;

(diff(diff(F(eta), eta), eta))*F(eta)-(diff(F(eta), eta))^2+beta*(diff(f(eta), eta)-(diff(F(eta), eta))) = 0

(2)

eq3 := (2*eta*gamma+1)*(1+Rd)*(diff(theta(eta), `$`(eta, 2)))+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+gamma*(diff(theta(eta), eta))+N*Pr*betat*((theta[p](eta), eta)-theta(eta))+N*Pr*Ec*betat*(diff(F(eta), eta)-(diff(f(eta), eta)))+Pr*delta*theta(eta) = 0;

(2*eta*gamma+1)*(1+Rd)*(diff(diff(theta(eta), eta), eta))+Pr*((diff(theta(eta), eta))*f(eta)-2*(diff(f(eta), eta))*theta(eta))+gamma*(diff(theta(eta), eta))+N*Pr*betat*((theta[p](eta), eta)-theta(eta))+N*Pr*Ec*betat*(diff(F(eta), eta)-(diff(f(eta), eta)))+Pr*delta*theta(eta) = 0

(3)

eq4 := 2*(diff(theta[p](eta), eta))*f(eta)-F(eta)*theta[p](eta)+betat*delta*(theta[p](eta)-theta(eta)) = 0;

2*(diff(theta[p](eta), eta))*f(eta)-F(eta)*theta[p](eta)+betat*delta*(theta[p](eta)-theta(eta)) = 0

(4)

bcs := f(0) = 0, (D(f))(0) = 1, (D(f))(5) = 0, (D(F))(5) = 0, F(5) = f(5), theta(0) = 1, theta(5) = 0, theta[p](5) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(5) = 0, (D(F))(5) = 0, F(5) = f(5), theta(0) = 1, theta(5) = 0, theta[p](5) = 0

(5)

params := [Rd = .1, beta = .5, Q = .5, S = .5, gamma = .1, Pr = 6.2, N = .5, betat = .5, Ec = .1];

[Rd = .1, beta = .5, Q = .5, S = .5, gamma = .1, Pr = 6.2, N = .5, betat = .5, Ec = .1]

(6)

sol := dsolve(eval([eq1, eq2, eq3, eq4, bcs], params), numeric, output = array([0]), maxmesh = 5000, initmesh = 1000)

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

``

Download MapleOde.mw

How to solve these systems of BVP and obtain values for gamma term.

Please help to solve the equation 

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Coefficients.mw .
 

Download Coefficients.mw

Hi 

I am a research scholar in mathematics

I am currently working on fluid mechanics

I wish to obtain the solution given in the research article

I am uploading the pdf containing problem.

In the paper they mentioned that " Shooting method" is used.

Please anyone help me regarding this topic

File : 1.pdf

Thank you

How to obtain a dual branch solution in Maple.

Is there any specific method is there to get these type of solutions.

I have attached the document.

Link [copyright material removed by moderator]

Thank you.

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